Is it any stranger than the United States for the United States of America, because it essentially is Saudi of Arabia, right?
He was not Saud of Arabia like Lawrence of Arabia, though; wiki names him Saud ibn Muhammad Al Muqrin— either way, the point is that that part of Arabia belongs to the Saud, rather than the other way around.
The English rendition is “the Kingdom of Saudi Arabia” - as you say, it’s the part of Arabia that is ruled by the House of Saud. But “Arabia” there is something of a false cognate. In English, “Arabia” is a larger region in which the Kingdom of Saudi Arabia is located. In Arabic, “as-Suʿūdīyah” is an adjective describing “al-Mamlakah” (“Kingdom”). The literal translation of the Arabic name would be more like, “the Saudi Arabian Kingdom”, or maybe “the Saudi and Arabian Kingdom”.
It may also be worth noting that KSA is one of the few absolute monarchies left. In a very real sense, the country belongs to the House of Saudi. Referring to it by the name of the royal family can be sort of a subtle commentary on that.
In Thailand I encountered lots of then-current and former Western workers who had spent lots of time in Saudi Arabia, and I think without exception they all called it Saudi. These were mostly not military people. None used the term in a derisive manner. You may say that doesn’t mean the Saudis themselves don’t consider it disrespectful, but the sense I got was that no one in the world considered it disrespectful.
How about Felix Arabia?
A subtle point. Arabic grammarians only recognize three parts of speech: nouns, verbs, and particles. Adjectives are classified under nouns. Not that they can’t tell the difference between adjectives and nouns, of course they can, but the reason is that the morphology of adjectives is functionally identical to that of nouns.
Which makes it easy for an adjective to simply function as a noun by itself, or else when put with a noun it can function as a modifier.
“al-Saʻūdīyah” in the full name is an adjective, but on its own it can be treated like a noun. Not strictly kosher as to nomenclature, but perfectly within the rules of Arabic grammar.
Arabia is a noun in English, but the word al-ʻArabīyah is an adjective that modifies al-Mamlakah ‘the kingdom’. So it’s sort of a false friend. The Latin -ia ending used to make place names is not the same as the Arabic -īyah ending for a feminine singular nisbah* adjective.
*Nisbah: Attributive derived from a noun by adding the suffix -ī (m.) īyah (f.)
Even in English, some adjectives can be used stand-alone as nouns. We speak of “the homeless”, “the elderly”, “the lives of the rich and famous”.
I believe this is done even more extensively in Hebrew, so I would not be surprised if the same is true in Arabic.
Now that you mention it… Even in L. A. (Los Angeles), L. A. is commonly referred to as “L. A.” (pronounced “ellay”, accent more-or-less on the second syllable).
San Luis Obispo is commonly locally called SLO, as in “Welcome to the SLO life!”
And Frisco is a real city – in Tejas!